Solve (3/2)^3-4(3/2)^2

$$( \frac { 3 } { 2 } ) ^ { 3 } - 4 ( \frac { 3 } { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{45}{8}=-5.625$$

Solution Steps

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{27}{8}-4\times \left(\frac{3}{2}\right)^{2}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{27}{8}-4\times \frac{9}{4}$$

Cancel out 4 and 4.

$$\frac{27}{8}-9$$

Convert 9 to fraction \frac{72}{8}.

$$\frac{27}{8}-\frac{72}{8}$$

Since \frac{27}{8} and \frac{72}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-72}{8}$$

Subtract 72 from 27 to get -45.

$$-\frac{45}{8}$$

Factor

$$-\frac{45}{8} = -5\frac{5}{8} = -5.625$$